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Published equation contexts

p^k+1=F(D0∪S1∪⋯∪Sk)\hat{p}_{k+1} = \mathcal{F}\left( D_0 \cup S_1 \cup \cdots \cup S_k \right)

Why this formula appears here

Change one term and the analysis changes with it. Consider instead p^k+1=F(D0∪S1∪⋯∪Sk)\hat{p}_{k+1} = \mathcal{F}\left( D_0 \cup S_1 \cup \cdots \cup S_k \right). where D0D_0 is the original real corpus and SjS_j the synthetic output of generation j . Gerstgrasser and colleagues make exactly this substitution and report that while replacing real data with each generation’s synthetic data does tend toward collapse, accumulating successive generations alongside the original real data avoids it — across transformers, diffusion models and variational autoencoders — and they prove that under accumulation the test error has a finite upper bound independent of the number of iterations [ 2 ] . The accumulating case is also the more accurate description of the actual web, which…

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p^k+1\hat{p}_{k+1}

Symbol hatp_k+1

hatpkp_k+1 is part of the quantity the equation computes from the expression on the right.

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Published contexts (1)

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p^k+1=F(D0∪S1∪⋯∪Sk),\hat{p}_{k+1} = \mathcal{F}\left( D_0 \cup S_1 \cup \cdots \cup S_k \right),

Equation 8 · Data & Training

Training on Your Own Output: Synthetic Data and What It Does to a Distribution

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Change one term and the analysis changes with it. Consider instead p^k+1=F(D0∪S1∪⋯∪Sk)\hat{p}_{k+1} = \mathcal{F}\left( D_0 \cup S_1 \cup \cdots \cup S_k \right). where D0D_0 is the original real corpus and SjS_j the synthetic output of generation j . Gerstgrasser and colleagues make exactly this substitution and report that while replacing real data with each generation’s synthetic data does tend toward collapse, accumulating successive generations alongside the original real data avoids it — across transformers, diffusion models and variational autoencoders — and they prove that under accumulation the test error has a finite upper bound independent of the number of iterations [ 2 ] . The accumulating case is also the more accurate description of the actual web, which…

Meanings in this article

  • F\mathcal{F}: the fitting procedure.
  • D0D_0: the original real corpus and SjS_j the synthetic output of generation j.
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